If you’re rich, you’re more lucky than smart. And there’s math to prove it | Hacker News Reader

If you’re rich, you’re more lucky than smart. And there’s math to prove it

pbs.org

50 pointslisper28 comments

I'm sympathetic to the above viewpoint, but the argument presented in the article sounds really dumb.

> "But think about it, the authors suggest. If smarts and talents and even effort are so normally distributed and wealth is so abnormally distributed, what’s missing to explain the disparity? “We suggest that such an ingredient is just randomness,” write the authors."

Just because talent is normally distributed, but outcomes are abnormally distributed, doesn't suggest in any way that this is caused by randomness. A winner-take-all game-format would perfectly describe the above phenomenon.

This can be trivially seen when the same logic is applied to sporting competitions. "If Tennis ability is normally distributed across the population, how can we explain a small handful of players like Federer and Williams winning an abnormally high number of championships? Clearly it must be because they're more lucky than talented."

Do you have any evidence that tennis skill is normally distributed?

The question whether it's normal distributed doesn't even make sense. Tennis skill and intelligence are both Ordinal Scales.

IQ is normal but that is just because we take everyones intelligences and assign them to a value from a normal distribution. http://www.mymarketresearchmethods.com/types-of-data-nominal...

What do you mean by an ordinal scale, and what does that imply? I'm completely blind on this usage of the expression.

It means that values are ordered, but not really numbers.

E.g. what does 2x better tennis skill mean?

An under that idea, the distribution curve doesn't really mean anything.

It would mean what this particular variable has been operationalized [0] to mean. Once upon a time things such as "heat" were just words, and as words they were used in a variety of different implicit senses in which at the time people didn't distinguish -- for whatever reason -- but that people thought that nonetheless were informative about the thing in question. Which is to say that words were used as heuristics, partly as reasonable descriptions, partly as expressions of gut feelings. With the association of heat with thermal expansion and the development of better apparatuses (e.g. the ordinary mercury column thermometers) as well as the diffusion of this concept among laymen though stuff such as weather prediction, it became the most salient form of "heat", and thus the standard use of the word when unqualified came to mean just that: what a thermometer reads. But other forms of heat i.e. the personal feelings of heat associated with climatic comfort, or the action of capsaicin or even wounds -- and this is the origin of the word "inflammation" -- came to be used only when qualified. These are all said to be "subjective heat". Now, I can only claim that all that I've said is merely opinion, since I haven't quite yet worked out to properly cite just who might have said this prior to me and for what reasons -- and which I currently wont, because it's scattered over stuff and I don't know even how to begin -- so this is all provided as is.

About ordinality, as opposed to cardinality, I can only say that I didn't see the connection at the beginning, but now that I've thought a little while about it, it does seem like a philosophically uncomfortable idea. But I'm not going to be the one to say why, at least not now.

[0]: https://en.wikipedia.org/wiki/Operationalization

It would be very strange if tennis skill was normally distributed. More than likely it’s a power law. Reaction time, physical strength and speed are normally distributed. The product of them will be approximately exponential. That’s almost certainly a better approximation of tennis skill. Ditto for likelihood to get rich. Intelligence, conscientiousness and luck for those. Luck is obviously an enormous factor in accumulating wealth. You’re a great deal more likely to get wealthy in the US than in Botswana and where you’re born and who you’re born to are luck.

You would see the same abnormally-distributed-outcomes in any winner-takes-all game where skill is normally distributed, and the higher-skilled-player always wins. The fact that skill is normally distributed but outcomes aren't, doesn't imply in any way that it's due to randomness.

In fact, the less random the game is, the more abnormal its outcome-distribution would be - the best player would win every single championship despite being just slightly better than the others.

Exactly. That wealth and intelligence distributions are different is simply evidence that wealth is not a simple linear function of intelligence.

Wealth might have multivariate interaction: luck, race, parentage, etc. Or have no other variable interactions with intelligence, but the intelligence relationship is non-linear.

Shoddy conclusion.

> A winner-take-all game-format would perfectly describe the above phenomenon.

That's not quite true, a winner-take-all with a normally distributed reward should probably also result in a normal distribution of wealth, due to the central limit theorem. If my memory serves me correctly - i am not a professional statistician - it's been long known (but also equally long forgotten) that markets (and for sure many natural risk distributions, like earthquakes), aka, rewards and penalties, are levy-distributed, which has undefined variance, resulting in a pareto distribution.

The model assigns opportunities every 6 months for 40 years and decides whether the talents of the potential beneficiary are adequate to exploit the opportunity.

It doesn't work this way. People waiting for opportunities don't encounter them with the same frequency as people actively looking for and/or trying to manufacture them. An opportunity for me to double my assets or income might exist, but will I even be aware of it? If I am, and my talent is adequate to exploit it, what kind of risk does it come with and what is my tolerance for such risk?

The last event in my life roughly conforming to the opportunities generated by this model was something I actively sought, carefully selected among hundreds of similar opportunities, and took enormous (stupid, I'd be saying now if it hadn't worked out) risk to exploit.

Opportunity comes for those who can seek it out, which predisposes a certain level of security (for most, though not all). Risk taking is done on a scale close to risk tolerance, and risk tolerance is higher when the downsides are slimmer.

I think the whole point of the paper which the writers at PBS might have glossed over is simply "we can reproduce this outcome with an extremely simple set of hypotheses". That's how I read it, at least, and that's something that's bound to cross the mind of someone familiar with agent based modelling. And if all they want is produce a power law distribution over income, that's all they need. Further model complications only become relevant if they lead off to new conclusions, or different outcomes from the generally expected outcome under particular circumstances. What you're suggesting would be, on the simple basis of some academic pragmatism -- and the fact that they still have to start from somewhere -- left to further studies, adding stuff to this model while citing the original paper.

But all that you're suggest would indeed bring back at least some degree of agency to the whole thing, even if just as being able to find, sort and act upon opportunities.

Some criticisms I have read about this paper include:

1) Their model assumes all persons start with the same initial wealth/capital, which is not true in real life

2) The model also assumes people's talent/ability remains constant and does not increase as they get older

In the end it is a model, and models are limited in how much they can match the real world. I do not believe the paper actually "proves" the hypothesis that "If you’re rich, you’re more lucky than smart" as the pbs.org title implies.

Starting with a higher capital is luck too though

By that measure, is not intelligence based on luck too?

As I have gotten older, I have made more money and gotten wealthier. My skills have increased, my knowledge has increased, and I am more valuable.

Did the authors look at wealth as something that is static and to be distributed? Or did they look at it as something that can be created (or destroyed)?

I reckon they have never actually ran a business or created any wealth themselves - but that is just a guess.

It's trivial to find someone that has equal skills that have either more wealth, or less. In fact, longer term studies have shown that wealth is inherited, and it takes I believe four generations to change from the lowest to the highest economic quintile. All of this is easily quantified, and has been repeatedly studied. The results are just sociopolitically unacceptable mythbusting. Read the wikipedia article on socioeconomic mobility [0], or perhaps the article about the economist that setup identical real world experiments, and found success was random chance.[1]

Anecdotally, the vast majority of the money I've come across in my life is pure luck. Skills, education, and not a sufficent (or even a necessary) condition of gaining wealth.

[0] https://en.wikipedia.org/wiki/Socioeconomic_mobility_in_the_... .

[1] https://www.npr.org/2014/02/27/282939233/good-art-is-popular...

I believe that the situation is simpler and more powerful than what the article claims.

Basically you need two things:

1) Some slight advantage

2) The network effect, that is, for example, the probability of competing depends on the current winnings.

If you have these two things, you get 80-20 like distributions, you get the explanation for why winners keep winning. If you are interested, you can find my simulation and analysis at

http://www.cs.toronto.edu/~arnold/research/80-20/

Kind of shocking how well this works. The intuition is, why has Coke won, well they had some initial advantage, and so they won a bit. Now that they have won a bit, they can finance themselves into more competition. For example, they can place themselves into more stores, into more restaurants etc. Now they get a chance to compete more. When I run with rules:

r1) Actors have normally distributed abilities,

r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete,

r3) Winner of competition wins one point from the loser,

You get interesting results, for example, in the two columns below, the left is Household income in 1970 broken into quintiles. The right column is simulation results.

    4.1%                         6.7%

   10.8%                        11.5%

   17.4%                        16.0%

   24.5%                        23.3%

   43.3%                        45.6%

Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.

If you run the simulation with different rules, the real world quintiles do not match the simulation quintiles nearly as well. You can tweak the simulation to see this as well.

The simulation can be tweaked to handle cases such as inheritance, so an actor with different ability inherits the wealth of a past actor. When I run this simulation, around 80-90% of top 20% actors lose all wealth in 3 generations. See for example:

https://www.theglobeandmail.com/globe-investor/globe-wealth/....

...having been born on 3rd base, she (or he) grew up thinking she had hit a triple... - (Various, 2013)

But think about it, the authors suggest. If smarts and talents and even effort are so normally distributed and wealth is so abnormally distributed, what’s missing to explain the disparity?

“We suggest that such an ingredient is just randomness,” write the authors

I think it's more due to the power of compounding. If you're a little tall, that doesn't help you get any taller. But, if you get a little rich, that helps you get richer, which helps you get even richer, and so on.

So many people assume that everyone wants to be rich. Some people don't. Many of the smartest never chased money.

And if you’re smart, that’s luck too. I didn’t earn my IQ.

Meritocracy man.